Characteristic analysis of a controlled-clearance piston-cylinder assembly up to 1500 MPa using a finite element method

Abstract

We utilized numerical methods to analyze the characteristics of the piston-cylinder assembly of a controlled-clearance piston gauge. The piston gauge was able to measure liquid pressure from 100 MPa to 1500 MPa with the relative expanded uncertainty of 0.02% (k = 3). We established a finite element model to solve the stress and strain of the structural problem. The effective areas were calculated based on Dadson’s formula using the converged solutions of the clearance and the pressure distribution within the distorted piston-cylinder engagement gap that were iteratively determined by the finite element model and a fluid mechanics model with pressure-dependent fluid’s properties. Results were compared to the effective areas calculated by the modified Heydemann–Welch model based on experimental data, and the relative differences were less than 0.02%. We found sharp declines of the clearance and pressure distribution near the exit of the piston-cylinder engagement gap, which may lead to wearing during long-time operation at high pressures. Numerical results indicated non-linear relationship between jacket pressure and the cubic root of piston fall speed, which was traditionally considered as linear. The stall jacket pressure obtained by cubic (instead of linear) fitting extrapolation was found more close to the ones determined directly by the finite element model. Numerical results also found non-linear relationships among jacket pressure, measuring pressure, jacket pressure distortion coefficient.